Implicit solvation in the self-consistent mean field theory method: sidechain modelling and prediction of folding free energies of protein mutants.

The Atomic Solvation Parameter (ASP) model is one of the simplest models of solvation, in which the solvation free energy of a molecule is proportional to the solvent accessible surface area (SAS) of its atoms. However, until now this model had not been incorporated into the Self-Consistent Mean Field Theory (SCMFT) method for modelling sidechain conformations in proteins. The reason for this is that SAS is a many-body quantity and, thus, it is not obvious how to define it within the Mean Field (MF) framework, where multiple copies of each sidechain exist simultaneously. Here, we present a method for incorporating an SAS-based potential, such as the ASP model, into SCMFT. The theory on which the method is based is exact within the MF framework, that is, it does not depend on a pairwise or any other approximation of SAS. Therefore, SAS can be calculated to arbitrary accuracy. The method is computationally very efficient: only 7.6% slower on average than the method without solvation. We applied the method to the prediction of sidechain conformation, using as a test set high-quality solution structures of 11 proteins. Solvation was found to substantially improve the prediction accuracy of well-defined surface sidechains. We also investigated whether the methodology can be applied to prediction of folding free energies of protein mutants, using a set of barnase mutants. For apolar mutants, the modest correlation observed between calculated and observed folding free energies without solvation improved substantially when solvation was included, allowing the prediction of trends in the folding free energies of this type of mutants. For polar mutants, correlation was not significant even with solvation. Several other factors also responsible for the correlation were identified and analysed. From this analysis, future directions for applying and improving the present methodology are discussed.